Mathematics

In the figure, $$x:y:z=5:4:6$$. If $$XOY$$ is a straight line, find the values of $$x,y$$ and $$z$$


SOLUTION
From the figure it is given that
$$x:y:z=5:4:6$$
We can also write it as
$$x+y+z=5+4+6=15$$
It is given that $$XOY$$ is a straight line
So we know that
$$x+y+z={ 180 }^{ o }$$

As we know that the sum of ratio is $$15$$ then we can write that the measure of $$x$$ as $$5$$
The sum of all the angles in a straight line is $${ 180 }^{ o }$$
So we get the measure of $$x$$ as
$$x=(5/15)\times 180$$
$$x=60$$

As we know the sum of ratio is $$15$$ then we can write that the measure of $$y$$ as $$4$$
The sum of all the angles in a straight line is $${ 180 }^{ o }$$
So we get the measure of $$y$$ as
$$y=(4/15)\times 180$$
$$y=48$$

In order to find $$z$$ we know that
$$x+y+z={ 180 }^{ o }$$
Substituting the values of $$x$$ and $$y$$ we get
$${60}^{o}+{48}^{o}+z={ 180 }^{ o }$$
$$z={ 180 }^{ o }-{60}^{o}-{48}^{o}$$
$$z={72}^{o}$$
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